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File:VFPt dipoles magnetic.svg

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Summary

Description
English: Computed drawings of four different types of magnetic dipoles.

Upper left: An ideal point-like dipole. The field shape is scale invariant and approximates the field of any magnetized volume with nonzero dipole moment at large distance.
Upper right: Discrete dipole of two opposite point-like magnetic poles at finite distance, a physical dipole. Note that isolated magnetic charges don't exist, but this configuration accurately represents the field of a very thin magnetized rod with magnetic poles at each end.
Lower left: Circular ring conductor loop with electric an current. An “Amperian loop”.
Lower right: Ideal continuous solenoid, a hollow cylinder with uniform circular current sheet around its circumference. This equally represents the B-field of a uniformely magnetized cylinder magnet.

Although the four field configurations differ significantly, they all converge to the same dipole field at large distances. Each configuration may represent a magnetic dipole.
Date
Source Own work
Author Geek3
Other versions VFPt dipoles electric.svg
SVG development
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The SVG code is valid.
 
This plot was created with VectorFieldPlot.
 
 This file is translated using SVG switch elements: all translations are stored in the same file.
Source code
InfoField

Python code

# paste this code at the end of VectorFieldPlot 2.5
R = 0.6
h = 0.6
rsym = 21


doc = FieldplotDocument('VFPt_dipoles_magnetic1', commons=True,
    width=360, height=360)
field = Field([ ['dipole', {'x':0, 'y':0, 'px':0., 'py':1.}] ])

def f_arrows(xy):
    return xy[1] * (sc.hypot(xy[0], xy[1]) / 1.4 - 1)
def f_cond(xy):
    return hypot(*xy) > 1e-4 and (fabs(xy[1]) < 1e-3 or fabs(xy[1]) > .3)

nlines = 19
startpoints = Startpath(field, lambda t: 0.25*sc.array([sin(t), cos(t)]),
    t0=-pi/2, t1=pi/2).npoints(nlines)
for p0 in startpoints:
    line = FieldLine(field, p0, directions='both')
    doc.draw_line(line, maxdist=1, arrows_style={'at_potentials':[0.],
        'potential':f_arrows, 'condition_func':f_cond, 'scale':1.2})

# draw dipole symbol
rg_grad = etree.SubElement(doc._get_defs(), 'linearGradient')
rg_grad.set('id', 'grad_rg')
for attr, val in [ ['x1', '0'], ['x2', '0'], ['y1', '0'], ['y2', '1'] ]:
    rg_grad.set(attr, val)
for col, of in [ ['#00cc00', '0'], ['#887744', '0.5'], ['#ff0000', '1'] ]:
    stop = etree.SubElement(rg_grad, 'stop')
    stop.set('stop-color', col)
    stop.set('offset', of)
    stop.set('stop-opacity', '1')
symb = doc.draw_object('g', {'id':'dipole_symbol',
    'transform':'scale({0},{0})'.format(1./doc.unit)})
doc.draw_object('circle', {'cx':'0', 'cy':'0', 'r':rsym,
    'fill':'url(#grad_rg)', 'stroke':'none'}, group=symb)
doc._check_whitespot()
doc.draw_object('circle', {'cx':'0', 'cy':'0', 'r':rsym,
    'fill':'url(#white_spot)', 'stroke':'#000000', 'stroke-width':'3'},
    group=symb)
doc.draw_object('path', {'fill':'#000000', 'stroke':'none',
    'd':'M 3,-12 V 0 H 12 L 0,15 L -12,0 H -3 V -12 H 3 Z'}, group=symb)
doc.write()



doc = FieldplotDocument('VFPt_dipoles_magnetic2', commons=True,
    width=360, height=360)
field = Field([ ['monopole', {'x':0, 'y':h, 'Q':1}],
    ['monopole', {'x':0, 'y':-h, 'Q':-1}] ])

def f_arrows(xy):
    return xy[1] * (sc.hypot(xy[0], xy[1]) / 1.4 - 1)
def f_cond(xy):
    return fabs(xy[0]) < 1.4

nlines = 18
stp = Startpath(field, lambda t: R*sc.array([.2*sin(t), 1+.2*cos(t)]),
    t0=-pi, t1=pi)
startpoints = [stp.startpos(s) for s in sc.arange(nlines)/float(nlines)]
startpoints.append(startpoints[nlines//2].dot([ [1,0],[0,-1] ]))
for p0 in startpoints:
    line = FieldLine(field, p0, directions='both', maxr=100)
    doc.draw_line(line, maxdist=1, arrows_style={'at_potentials':[0.],
        'potential':f_arrows, 'condition_func':f_cond, 'scale':1.2})

# draw pole symbols
symb_N = doc.draw_object('g', {'id':'north_symbol',
    'transform':'translate(0,{0}) scale({1},{1})'.format(h, 1./doc.unit)})
symb_S = doc.draw_object('g', {'id':'south_symbol',
    'transform':'translate(0,{0}) scale({1},{1})'.format(-h, 1./doc.unit)})
for i, g in enumerate([symb_N, symb_S]):
    doc.draw_object('circle', {'cx':'0', 'cy':'0', 'r':rsym, 'stroke':'none',
        'fill':['#ff0000', '#00cc00'][i]}, group=g)
    doc._check_whitespot()
    doc.draw_object('circle', {'cx':'0', 'cy':'0', 'r':rsym,
        'fill':'url(#white_spot)', 'stroke':'#000000', 'stroke-width':'3'}, group=g)
    
    text = etree.SubElement(g, 'text')
    for attr, val in [ ['text-anchor', 'middle'], ['x', 0], ['y', 11],
        ['fill', '#000000'], ['stroke', 'none'], ['font-size', '32px'],
        ['font-family', 'Bitstream Vera Sans'],
        ['transform', 'scale(1, -1)'] ]:
        text.set(attr, str(val))
        text.text = ['N', 'S'][i]
doc.write()



doc = FieldplotDocument('VFPt_dipoles_magnetic3', commons=True,
    width=360, height=360)
field = Field([ ['ringcurrent', {'x':0, 'y':0, 'R':R, 'phi':pi/2, 'I':1.}] ])

def f_arrows(xy):
    return xy[1] * (sc.hypot(xy[0], xy[1]) / 1.4 - 1)
def f_cond(xy):
    return hypot(*xy) > R and fabs(fabs(xy[0]) - 1.4) > 0.2

nlines = 13
startpoints = Startpath(field, lambda t: sc.array([R*t, 0.]),
    t0=-0.8, t1=0.8).npoints(nlines)
for p0 in startpoints:
    line = FieldLine(field, p0, directions='both')
    doc.draw_line(line, maxdist=1, arrows_style={'at_potentials':[0.],
        'potential':f_arrows, 'condition_func':f_cond, 'scale':1.2})

# draw current symbols
symb_out = doc.draw_object('g', {'id':'out_symbol',
    'transform':'translate({0},0) scale({1},{1})'.format(-R, 1./doc.unit)})
symb_in = doc.draw_object('g', {'id':'in_symbol',
    'transform':'translate({0},0) scale({1},{1})'.format(R, 1./doc.unit)})
for i, g in enumerate([symb_out, symb_in]):
    doc.draw_object('circle', {'cx':'0', 'cy':'0', 'r':rsym, 'stroke':'none',
        'fill':'#999999'}, group=g)
    doc._check_whitespot()
    doc.draw_object('circle', {'cx':'0', 'cy':'0', 'r':rsym,
        'fill':'url(#white_spot)', 'stroke':'#000000', 'stroke-width':'3'}, group=g)
    
    if i == 0: # dot
        c_symb = etree.SubElement(g, 'circle')
        c_symb.set('cx', '0')
        c_symb.set('cy', '0')
        c_symb.set('r', '6')
    else: # cross
        c_symb = etree.SubElement(g, 'path')
        c_symb.set('d', 'M {1},{4} L {0},{5} L {2},{3} L {0},{1} \
L {1},{0} {3},{2} L {5},{0} L {4},{1} L {6},{3} L {4},{5} L {5},{4} \
L {3},{6} L {1},{4} Z'.format(12.24, 8, 4.24, 0, -12.24, -8, -4.24))
        c_symb.set('style', 'fill:#000000; stroke:none')
doc.write()



doc = FieldplotDocument('VFPt_dipoles_magnetic4', commons=True,
    width=360, height=360)
field = Field([ ['coil', {'x':0, 'y':0, 'phi':pi/2, 'R':R, 'Lhalf':h, 'I':1.}] ])

def f_arrows(xy):
    return xy[1] * (sc.hypot(xy[0], xy[1]) / 1.4 - 1)
def f_cond(xy):
    return sc.hypot(xy[0], xy[1]) > R

nlines = 13
for iline in range(nlines):
    p0 = sc.array([R * (-1. + 2. * (iline + 0.5) / nlines), 0.])
    line = FieldLine(field, p0, directions='both', maxr=100)
    doc.draw_line(line, maxdist=1, arrows_style={'at_potentials':[0.],
        'potential':f_arrows, 'condition_func':f_cond, 'scale':1.2})

# draw solenoid
sheet_out = doc.draw_object('g', {
    'transform':'translate({0},0)'.format(-R)})
sheet_in = doc.draw_object('g', {
    'transform':'translate({0},0)'.format(R)})
for i, g in enumerate([sheet_out, sheet_in]):
    doc.draw_object('rect', {'stroke-width':0.03, 'stroke-linejoin':'round',
        'x':-0.045, 'y':-h, 'width':0.09, 'height':2*h,
        'stroke':'#000000', 'fill':'#bbbbbb'}, group=g)
    nsym = 12
    for isym in range(nsym):
        y = (h - 0.015) * (2 * (isym + 0.5) / nsym - 1)
        if i == 0:
            doc.draw_object('circle', {'cx':'0', 'cy':y, 'r':0.02,
            'fill':'#000000', 'stroke':'none'}, group=g)
        else:
            doc.draw_object('path', {'d':'M -2,-2 L 2,2 M -2,2 L 2,-2',
                'fill':'none', 'stroke':'#000000',
                'transform':'translate(0, {0}) scale(0.012)'.format(y),
                'stroke-width':'1', 'stroke-linecap':'butt'}, group=g)
doc.write()

Licensing

I, the copyright holder of this work, hereby publish it under the following license:
w:en:Creative Commons
attribution share alike
This file is licensed under the Creative Commons Attribution-Share Alike 4.0 International license.
You are free:
  • to share – to copy, distribute and transmit the work
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Under the following conditions:
  • attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
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Captions

Four models of magnetic dipoles with accurately computed field lines

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inception

11 January 2020

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Date/TimeThumbnailDimensionsUserComment
current16:25, 11 January 2020Thumbnail for version as of 16:25, 11 January 2020840 × 840 (103 KB)Geek3User created page with UploadWizard
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